Being honest - it doesn't sound like you love him, but rather want to stay in his nice house.
Regardless of if you love him or not, that trust that's needed for a stable, long-term relationship has been obliterated. Every single thing you do will be questioned, outloud or at least subconsciously. That is not going to be good for a healthy relationship.
I'd suggest that if you want to be in a happy and healthy relationship, it's probably a good idea to move on from this one. Take time to reflect and ask yourself why you cheated on this guy - obviously you were unhappy enough to seek someone else, but what made you unhappy in the first place? It could be something about them, but it could be something about yourself too - in which case, you might want to talk to a therapist
If you did want to get back with your ex, I'd suggest giving him space and letting him decide if he wants to come back to the table, and when he wants to. If you seriously like him, don't see anyone else until he decides what he wants to do; but put a time limit on it for your own sanity. Then, after the time is up, give up on the relationship and move on. Tell a friend of yours about your plan so they can help keep you accountable in case you may not be in the right frame of mind